Te Huihuinga i te Wā Roa: Te Ture o ngā Tau Nui i te Rūreti
Te āhua o te toharite e tau haere ana ki te −2.70%, me te take e roa ake ai tēnā i tā te whakaaro tūturu e matapae ai.
Ka tata haere te ngaronga toharite mō ia hurihanga ki te −1/37 i te piki haere o ngā hurihanga, ā, ka mimiti tōna hora pērā i te 1/√N. I muri i ngā hurihanga whero 1,000, kei roto te toharite i te ±3% o tōna uara tūmanako i te nuinga o te wā.
Ture o ngā tau nui
Ka anga te toharite haere o ngā peti motuhake ki te uara tūmanakopāngarauUara tūmanakoTe hua toharite mō ia peti i te wā roa. −1/37 o te moni peti mō ia peti Ūropi paerewa.Pānuitia katoatia →. I muri i ngā hurihanga utu ōrite N ki te waemoniWaeTe moni peti taketake e mahi ai tētahi pūnaha, tētahi kaitākaro rānei. Ka whakaahuatia ngā kauneke ki ngā wae kia hāngai ai ki ia tēpu.Pānuitia katoatia → kotahi, ko te tūmanako o te hua toharite mō ia hurihanga ko te −1/37, ā, ko tōna hipanga paerewapāngarauHipanga paerewaTe pūtake rua o te tītaringa; te tawhiti noa o te hua i te uara tūmanako.Pānuitia katoatia → ko te 1/√N. I te N = 100, ko taua hora te 10% o te moni peti, tata ki te whā whakarea o te tohu 2.7%. I te N = 1,000, ko te 3.2%, he ōrite tata ki te tohu. I te N = 10,000, ko te 1%, ā, e kitea mārakerake ana te painga. Kāore e kitea te painga i roto i te wā tākaro kotahi, engari kāore e taea te pōhēhē i roto i te tau kotahi.
Ko te aha e tata haere ana, ko te aha kāore
Ka tata haere te toharite mō ia hurihanga. Kāore te tapeke: ka kotiti haere kē atu i te kore i te tupu o te N, mā te 2.7% o te N tata nei i te tūmanako, me te hora √N huri noa i tērā. Ko te kaitākaro kua tākaro i ngā hurihanga 10,000 ki te $10, e tūmanakohia ana ka heke ia $2,700, tāpiri atu, tango atu rānei te $1,000. Kua roa kē te ōwehenga haere o ngā wheropetiWheroHe peti utu ōrite ki ngā tau whero e 18. Wīwī: rouge.Pānuitia katoatia → e tau ana ki te 48.65%; kāore anō te toenga haere kia tau ki hea rawa.
- p10 −$440
- p25 −$280
- tau waenga −$140
- p75 +$0
- p90 +$140
He aha i hapa ai te whakaaro tūturu
E tūmanako ana te tangata ka puta wawe te painga nā te mea he āhua nui te 2.70% ki te taringa, ā, e tūmanako ana ka “ōrite haere” ngā raupapa roa nā te mea e kī ana te ture o ngā tau nuipāngarauTure o ngā tau nuiKa tata atu te toharite o ngā hua motuhake ki te uara tūmanako i te tipu o te maha o ngā whakamātautau.Pānuitia katoatia → ka tata haere ngā toharite. Ka hē te rahinga i ngā whakaaro e rua: he iti te painga ki te taha o te tītaringapāngarauTītaringaHe inenga o te whānui o te marara o ngā hua huri noa i te uara tūmanako. He teitei mō te tau kotahi, he hakahaka mō ngā peti utu ōrite.Pānuitia katoatia → o te hurihanga kotahi (σ = 1 wae ki te EV = 0.027), nō reira e (1/0.027)² ≈ 1,400 ngā hurihanga kia kitea ai i te taumata kotahi-sigma. Ā, kāore te tata haere o te toharite e kukume i te tapeke ki muri; ka whakaiti noa i ngā piki me ngā heke o mua.
Te tata haere mō ētahi atu peti
Mō ngā peti tau kotahipetiTau kotahiHe tau kotahi, ko te utunga 35:1.Pānuitia katoatia → ko te σ = 5.84, nō reira ka puta i taua tātai anō te (5.84/0.027)² ≈ 47,000 hurihanga kia tae te painga ki te sigma kotahi. Ka taea e te kaitākaro tau kotahi te tākaro mō ngā tau maha kāore e taea te wehe i te painga i te waimarie i roto i āna ake rekoata, ahakoa e utu ana ia i te 2.70% ōrite tonu ki te kaitākaro whero e kite ana i roto i ētahi wiki.
Te tikanga mō te whakamātautau pūnaha
Ko te tangata e kī ana e whai hua ana tētahi pūnaha, me taea e ia te whakaatu i ngā hurihanga 10,000, neke atu rānei, me tētahi toharite tōrunga kua tuhia. I ngā hurihanga 1,000, ko te toharite tōrunga i te utu ōrite he takahanga kotahi i te rima i raro i te whakapae kore; i ngā hurihanga 100, he ōrite tata ki te maka moni. Ka whakahaere ngā taputapu whaihanga o tēnei pae i ngā wā tākaro 2,000 o te roa i kōwhiria e koe i roto i te hēkona kotahi, ā, he nui ake tēnā taunakitanga i tētahi kōrero whakaatu.
Tātai
Ngā pātai
Ka heke te tūponotangapāngarauTūponotangaTe tūpono o tētahi putanga, mai i te 0 ki te 1, mai i te 0% ki te 100% rānei. Tau kotahi: 1/37 = 2.70%.Pānuitia katoatia → o te piki ake anō ki te kore i a koe e tākaro ana. Ka heke haere te tapeke me te kore tepe.
Kāo. Ko te tikanga ka iti haere te hautanga o ngā piki me ngā heke o mua i roto i tētahi tauira nui ake.
Mō te utu ōrite, tata ki te 10,000 i mua i te kitea mārakerake o te painga. Mō ngā tau kotahi, tata ki te 50,000.
He Pārekareka te Pāngarau
Me whakamātau koe i ēnei i te tuatahi. Kua kōpakina ia otinga; whakatuwherahia ina rite koe.
Ka tākaro ngā hoa tokorua i ngā rauna 20 o tētahi kēmu tōkekepāngarauKēmu tōkekeHe kēmu kāore he painga ki tētahi taha: he kore te uara tūmanako o ia peti.Pānuitia katoatia →, he whiu moni, he wheropetiWheroHe peti utu ōrite ki ngā tau whero e 18. Wīwī: rouge.Pānuitia katoatia → rānei ki te pangopetiPangoHe peti utu ōrite ki ngā tau pango e 18. Wīwī: noir.Pānuitia katoatia → me te whakahoki i ngā korewīraKoreTe kōhao kākāriki kotahi kāore e kapia e tētahi peti utu ōrite, tatini, tīwae rānei; te pūtake o te painga o te whare. Arā anō: kore kotahi, 0.Pānuitia katoatia →, ā, ka puritia he kaute haere tonu. Tatauria ngā rauna kei mua ia tangata (ka kautehia te ōrite mō te tangata i mua i te rauna i mua tonu atu). Ko tēhea te tūpono nui ake: ka wehea te tūranga mātāmua 10 rauna ki te 10, ka mātāmua rānei tētahi hoa i ngā 20 katoa?
Whakaaturia te otinga
Whakautu He nui kē atu te tūpono ka mātāmua tētahi hoa i ngā rauna 20 katoa: 35.2%, ahakoa ko tēhea hoa, ki te whakatauritea ki te 6.1% mō te 10 ki te 10 ōrite.
Ko te tūpono ka ōrite te kaute haere tōkeke i muri i ngā rauna 2k ko te u = C(2k, k)/2²ᵏ: 0.246 i muri i ngā rauna 10, ā, 0.176 i muri i ngā 20. E ai ki tētahi hua rongonui, te ture arc-sine, ko te tūpono ka mātāmua tētahi hoa kua whakaingoatia mō ngā rauna 2k tonu o ngā 2n ko te u(2k) × u(2n − 2k).
Mātāmua i ngā 20 katoa: u(20) × u(0) = 0.176 mō ia hoa, 35.2% mō tētahi o rāua. He wehenga ōrite: u(10) × u(10) = 0.246² = 6.1%, te wehenga iti rawa te tūpono o te katoa.
Nō reira i te kēmu tōkeke he onge te whakawhiti o te tūranga mātāmua. Ko te kaitākaro kua noho ki mua i te pō katoa, ki muri rānei i te pō katoa, kāore he mea rerekē kua kitea e ia, ā, kāore he kōrero mō te wīra, mō te pūkenga rānei. Ka hoatu e Epstein (2013) taua ture anō mō ngā kēmu roa ake: i te haurua o te wā ka mātāmua te taha waimarie ake mō te nui ake i te 85% o te tākaro.
He katakata iti
Ka tata haere te toharite. Ko te tapeke, ka haere kē atu.
Ngā Puna
- Bernoulli, J. Ars Conjectandi.
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.